Market-Oriented Programming Method applied in Distributed Energy Managment Programme
Abstract: Control of CO 2 emissions which is the main factor of global warming is one of the most important problems in the 21st century about preservation of earth environment. Therefore, efficient supply and use of energy are indispensable. We have proposed distributed energy management systems (DEMSs), where we are to obtain optimal plans that minimize both of costs and of CO 2 emissions through electrical and thermal energy trading. A DEMS consists of the plural entities that seek their own economic profits. In this paper, we propose a trading method that gives competitive equilibrium resource distribution by applying the market-oriented programming (MOP) to DEMSs
This topic discusses energy planning in a small district composed of a set of corporate entities.
Although the term “energy planning” has a number of different meanings, the energy planning in this chapter stands for ﬁnding a set of energy sources and conversion devices so as to meet the energy demands of all the tasks in an optimal manner. Since reduction of CO2 emissions which are the main factor of global warming is one of the most important problems in the 21st century about preservation of the earth environment, recent researches on energy planning consider reducing impacts to the environment(Cormio et al., 2003; Dicorato et al., 2008; Hiremath et al., 2007).
On the other hand, corporate entities with energy conversion devices become possible to sale surplus energy by deregulation about energy trading. Normally conversion devices have non-linear characteristics; its efﬁciency depends on the operating point. By selling energy to other entities, one may have an opportunity to operate its devices at a more efﬁcient point.
We suppose a small district, referred to be a “group”, that composed of independent plural corporate entities, referred to be “agents”, and in the group trading of electricity and heat energies among agents are allowed. We also suppose that a cap on CO2 emissions is imposed on each agent. Each agent performs energy planning under the constraints on CO2 emissions and by considering energy trading in the group.
An agent may take various actions for reduction: use of alternative and renewable energy sources, use of or replacement to highly-efﬁcient conversion devices, purchase of emission credits, and soon. Use of alternative and renewable energy sources and purchase of emission credits are easier ways to reduce CO2 emissions. However, there is no guarantee to get sufﬁcient amount of such energy or credit at an appropriate price, because the amount of such energy and credit is limited and their prices are resolved in the market. On the other hand, installing a highly-efﬁcient conversion device comes expensive.
Another way to reduce CO2 emissions is energy trading among agents. Suppose that one agent is equipped with an energy conversion device such as boilers, co-generation systems, etc. If he operates his device according to his energy demands only, the operating point of the device cannot be the most efﬁcient one. Energy trading among agents makes it possible to seek efﬁcient use of devices, and as a result to reduce CO2 emissions.
When we attempt to minimize energy cost under the constraints on CO2 emissions in the group, it is not difﬁcult by considering the entire group as one agent. But it is another matter whether each agent will accept the centralized optimal solution because agents are independent. Therefore, we adopt a cooperative energy planning method instead of total optimization. By this method, we want to reduce energy consumption considering the amount of the CO2 emissions in the entire group without undermining the economic beneﬁt to each agent. A software system in the control center in a power grid to control and optimize the performance of the generation and/or transmission system is known as an energy management system (EMS). We are considering a distributed software system that performs energy planning in the group. We call such a energy planning system for the group a distributed energy management system (DEMS).
Corresponding mathematical formulation of the energy planning is known as the unit commitment (UC) problem(Padhy, 2004; Sheble & Fahd, 1994). Although the goal of our research is solving the UC problem and deciding the allocation of traded energies in DEMSs, the main topic of this chapter is to discuss how to ﬁnd an optimal energy allocation. In order to make the problem simple, we consider the UC problem with only one time period and all of the energy conversion devices are active. Most methods for the UC problem solve in centralized manner. But as mentioned before we cannot apply any centralized method. Nagata et al. (2002) proposed a multi-agent based method for the UC problem. But they did not consider energy trading among agents.
The interest of this chapter is how to decide the allocation of traded energies through coordination among agents. In DEMSs, an allocation that minimize the cost of a group is preferred; a sequential auction may be preferred. Therefore, we propose to apply the market-oriented programming (MOP)(Wellman, 1993) into DEMSs.
The MOP isknown as a multi-agent protocol for distributed problem solving, and an optimal resource allocation foraset of computational agents is derived by computing general equilibrium of an artiﬁcial economy. Some researches, which uses the MOP, have been reported in the ﬁelds of the supply chain management (Kaihara, 2001), B2 Bcommerce (Kaihara, 2005), and so on. Maiorano et al. (2003) discuss the oligopolistic aspects of an electricity market.
This chapter is organized as follows. Section 2 in troduces the DEMSs and an example group. An application of the MOP into DEMSs is described in Section 3. The bidding strategy of agents and an energy allocation method based on the MOP is described. In Section 4, computational evaluation of the MOP method is performed comparing with three other methods. The ﬁrst comparative method is an multi-items and multi-attributes auction-based method. The second one is called the individual optimization method, and this method corresponds to a case where internal energy trading is not allowed. The last one is the whole optimization method.
2. Distributed Energy Management Systems
A software system in the control center in a power grid to control and optimize the performance of the generation and/or transmission system is known as an energy management system (EMS). This chapter addresses an operations planning problem of an EMS in independent corporate entities. Each of them demands electricity and heat energies, and he knows their expected demand curves. Moreover a cap on CO2 emissions is imposed on each entity, and it is not allowed to exhaust CO2 more than their caps. Some (or all) entities are equipped with energy conversion devices such asturbines; they perform optimal planning of purchasing primal energy and operating energy conversion devices in order to satisfy energy demands and constraints on CO2 emissions.
We suppose a small district, referred to be a “group”, that composed of independent plural corporate entities, referred to be “agents”, and in the group trading of electricity and heat energies among agents is allowed. In the case of co-generation systems, demands should be balanced between electricity and heat in order to operate efﬁciently. Even when demands from himself are not balanced, if an agent was possible to sell surplus energy in the group, efﬁciency of the co-generation system might be increased. Normally conversion devices have non-linear characteristics; its efﬁciency depends on the operating point. By selling energy to other entities, one may have an opportunity to operate its devices at a more efﬁcient point. There is a merit for consumers that they are possible to obtain energies at a low price.
It is possible to consider the whole group to be one agent, and to perform optimization by a centralizedmethod,referredtobea“wholeoptimization”. Thewholeoptimizationcomesup with a solution which gives the lower bound of group cost; since each agent is independent, there exists another problem that each agent accepts the solution by the whole optimization or not.
The DEMS is a software (multi-agent) system that seeks optimal planning of purchasing primal energy and operating energy conversion devices in order to satisfy energy demands and constraints on CO2 emissions by considering energy trading in the group. The cost for each agent is deﬁned by the difference between the total cost of purchased energy and the income of sold energy; the cost of the group is deﬁned by the sum of agent’s costs. We are expecting that the group cost is minimized as a result of proﬁt-seeking activities of agents.
Generally, energy demands are time varying and cost arises at starting conversion devices up. Although the goal of our research is solving the UC problem and deciding the allocation of traded energies in DEMSs, the main topic of this chapter is to discuss how to ﬁnd an optimal energy allocation. In order to make the problem simple, we consider the UC problem with only one time period and all of the energy conversion devices are active.
In DEMSs, since a cap on CO2 emissions is imposed on each agent, it is necessary that a producer is able to impute his overly-emitted CO2 to consumers in energy trading. Therefore, we employ not only the unit price but also the CO2 emission basic unit for energy trading. The CO2 emission basic unit means the amount of CO2 emitted by energy consumption of one unit. Power companies and gas companies calculate CO2 emission basic unit of their selling energies in consideration of relative proportions of their own energy conversion devices or constituents of products, and companies have been made them public. Consumers are possible to calculate their CO2 emissions came from their purchased energy. Note that CO2 emission basic unit is considered just as one of attributes of a energy in DEMSs, and its value could be decided independent of relative proportions of energy conversion devices or constituents of products.
In a group, agents are connected by electricity grids and heat pipelines; they are able to transmit energies via these facilities. The electricity grid connects each pair of agents, but the heat pipeline is laid among a subset of agents. We do not take capacities of electricity grids and heat pipelines into account; also no wheeling charge is considered.
Figure 1 depicts an example group that is a subject of this chapter. This group is composed of three agents: Factory1, Factory2, and Building. The arrows indicate energy ﬂows; two factories purchase electricity and gas from outside of the group and sell electricity and heatin the group, and Building purchases electricity, gas and heat from both of inside and outside of the group. Composition of each agent is shown in Fig.2 and Fig.3. BA is aboiler and GTisagas-turbine. BEe and BE express electricity purchased from outside and inside of the group, respectively. BG expresses gas purchased from outside of the group; BH expresses heat purchased from
inside of the group. PH is the produced heat and PE is the generated electricity. DE, DH, and WH express electricity demand, heat demand, and waste heat, respectively. Building tries to meet his electricity demand by purchasing electricity from inside and outside of the group, and he tries to meet his heat demand by producing heat with his boiler and by purchasing heat in the group. Factories tries to meed his electricity demand by generating electricity with his gas-turbine and by purchasing electricity from outside of the group, and he tried to meet his heat demand by producing heat with his boiler and/or gas-turbine.
3. Application of the Market-Oriented Programming into DEMSs
3.1 Market-Oriented Programming
The Market-Oriented Programming (MOP)(Wellman, 1993) is a method for constructing a virtual perfect competitive market on computers, computing a competitive equilibrium as a result of the interaction between agents involved in the market, and deriving the Pareto optimum allocation of goods. For formulation of the MOP, it is necessary to deﬁne (1) goods, (2) agents, and (3) agent’s bidding strategies.
A market is opened for each good, and the value (unit price) of a good is managed by the market. Each agent cannot control the value, and he makes bids by the quantity of goods in order to maximize his own proﬁt under the presented values. Each market updates the value in compliance with market principles (Fig. 4). Namely, when the demand exceeds the supply, the market raises the unit price; when the supply exceeds the demand, the market lowers the unit price. The change of unit price is iterated until the demand is equal to the supply in all markets; the state is called an equilibrium.
3.2 Formulation of Markets
For the formulation of MOP, we deﬁne (1) goods (2) agents, and (3) agent’sbiddingstrategies as follows:
Electricity and heat traded in the group are goods.
(2) agents A corporate entity in the group is an agent, and an agent that has energy converters such as turbines can be comeaproducerora consumer, but it can not be aproducer and a consumer at the same time.
(3) agent’s bidding strategies Bidding strategies will be described in Section 3.3.
3.3 Bidding Strategies
Each agent ﬁnds the amount of purchased/sold energies and input energies for his conversion devices that minimize his own cost under the constraints of energy balance, the cap on CO2 emissions, characteristics of devices. Bidding strategies of agents introduced in Section 2.2 could be expressed as follows.
3.4 Demand-Supply Curves
It is know that one of necessary conditions for the convergence of the MOP is convexity of the production possibility set (Wellman, 1993). The characteristic function of energy conversion devices is important of the convexity. For example, when the function is given by Equation (10), the parameter b must hold that b < 1. A typical example of demand-supply curves in DEMSs is shown in Fig. 5. There exist two characteristics in DEMSs.
The ﬁrst characteristic is that the demand (resp. supply) curve has a gap in the amount between 0 and some positive value at the price α (resp. α). This is caused by that agents tries to maximize their economic proﬁts. Namely, α and α are marginal prices so that agents are able to make a proﬁt. It is proﬁtable for a consumer to purchase the energy in the group when the price is lower than α, then he will bid a positive value. If the price is higher than α, it is profitable to purchase the energy from outside of the group, then his bid will become 0. Similarly, a producer will not supply energy in the group when the price is lower than α. The second characteristic is that there exists a upper limit of the amount for both of the demand and the supply curves. The upper limit for the demand curve comes from the energy demand of consumers, and the upper limit for the supply curve comes from capacities of energy conversion devices.
3.5 Execution Procedure
Due to the characteristics described in Section 3.4, a case may happen that no crossing exists, therefore a simple MOP procedure does not converge to the equilibrium. There exist two types for such a situation. 1. Over-demand at α (Fig. 6) When producers are notable to supply enough energy to meet the demand of consumer agents, the demand exceeds the supply even at (just below of) α. At the next turn, the price becomes a little bit higher than α, then the demand becomes 0. Therefore vibration of price may appear.
In this case, the supplied energy is shared among consumer agents and the shortage must be managed by other methods. By introducing a cap on the demand in the MOP procedure, we realize that.
2. Over-supply at α (Fig. 7)
When suppliers produce anample of energy, the amount of the supply may exceeds the demands at (just above of) α. At the next turn, the price becomes a little bit lower than α, then the supply becomes 0. Also in this case, vibration of price may appear.
This kind of situation may occur when a supplier hold a co-generation system and his heat demand is not much. He operate the co-generation system in order to meet the electricity demand. But at the same time, plenty of heat will also produced. Hemaysell the heat even if the price is 0, but may not sell when the price becomes negative. In this case, the energy demand is shared among producer agents and the rest is dumped. By introducing a cap on the supply in the MOP procedure, we realize that.
4. Computational Experiments
4.1 Energy Trading Decision Methods
This section introduces other energy allocation methods briefly.
4.1.1 Individual Optimization
Under the individual optimization method, each agent purchases energy only from outside of the group, and optimizes its running plan of conversion devices. By using this method, we can calculate group cost and cost for each agent under a condition that internal energy trading is not used.
4.1.2 Whole Optimization
The whole optimization method considers the group as one agent, and does optimization for the whole group. In this case the cap on emissions is imposed on the whole group. We can calculate lower bound cost for the group by using this method. This lower bound is optimal, and we cannot get better plan than that. With this method, we can get an energy purchase and running plan of devices, but we cannot get cost and CO2 emission for each agent.
4.1.3 Multi-attribute and Multi-item Auction Miyamoto et al. (2007) proposed an energy trading decision method based on English auction protocol (David et al., 2002). This method is a multi-attribute auction because it uses two attributes: unit price and CO2 emission basic unit. Also it is a multi-item auction because energy demands could be divided into several demands with small energy amount.
This method expresses energy value by
ν = λα + µβ, (30)
where α is unit price, β is CO2 emission basic unit, and λ and µ are parameters. A consumer shows three items: amount of energy demand, λ and µ. Producers bid three items: their amount of energy supply, α, and β. After some iterations, winning producers get rights to supply.
When an agent holds a conversion device, such as a gas turbine, that is able to produce more than one types of energy, electricity trading and heat trading are inseparable for the agent.
Therefore, in (Miyamoto et al., 2007) we adopted a sequential method; we decide electricity trading first and then decide heat trading.
In the following experiments, we used parameters shown in Tables 1 and 2.
Table 1 shows unit price and CO2 emission basic unit of electricity and gas purchased from outside of the group. These values are taken from Web pages of power and gas company in Japan.
Table 2 shows parameters of conversion devices, where PHBA is the maximum output heat of the boiler, and PEGT is the maximum output electricity of the gas-turbine.
4.3 Ex1: Evaluation of Concurrent Evolution
This experiment is done in order to evaluate the concurrent evolution of electricity and heat trading. Table 3 shows energy demands and the cap on CO2 emissions for each agent.
Experimental results are shown in Tables 4, 5, 6, and 7.
By the auction method (Table 5), the producer agent assumes that amount of heat trade is zero when the agent calculate a bid for electricity auction. The agent cannot allow for emissions reduction through heat trading, and electricity sales of Factory 2 resulted in only 4748.1[kWh].
The agent cannot produce further electricity due to the caps.
On the other hand, Factory 2 succeeded to sell electricity of 10000[kWh] by the MOP method (Table 4), because the agent could take emissions reduction through heat trading into consideration. This trade could not be achieved through sequential method such as the auction method. The MOP method succeeded to obtain better solution by deciding electricity and heat trade concurrently.
The whole optimization method worked out an optimal solution (Table 6), and Factory 1 which has the most efficient gas turbine produced most electricity and heat for Building. As a result, the group does not buy any electricity from the outside. As for group costs, we can say that group cost by the MOP method is not so different from cost by the whole optimization.
Note that this method cannot decide the cost and CO2 emissions for each agent.
The resulting plan by the individual optimization was expensive because internal energy trading was not used. The result (Table 7) shows effectiveness of the internal energy trading.
4.4 Ex2: Evaluation for Consumer’s Demand Change This experiment is done in order to evaluate efﬁciency of the methods under a change of consumer’s demands. Energy demands and caps on CO2 emissions for each agent are shown in Table 8. We ﬁxed electricity demand and increased head demand by 10000[Mcal] of Building who is a consumer in the group. In this case, factories begin to start their boiler as electricity demand increases. In order to exclude inﬂuences of emissions constraints, the cap on emissions for Building was set enough large as 35000[kg-CO2].
4.4.1 Comparison on Group Cost
Figure 9 shows transitions of group costs by each method when heat demand of Building changes. Costs by all methods except the individual optimization are constant until 90000[Mcal]. This is because heat was over produced in order to produce electricity and internal trading of heat does not effect the group costs. When heat demand exceeds 100000[Mcal],agents have to start their boiler to meet the heat demand, and then the group costs increases. In comparison to the individual optimization,which does not use internal trading, other three methods succeeded to reduce the group costs. This result shows that it is possible to reduce a group cost by intro ducing internal energy trading. For every heat demands,the MOP method obtains near optimal solutions, and they were better than the solutions by the auction method. This is an effect of the concurrent evolution.
4.4.2 Comparison on Agent Costs
Figure 10 shows transitions of CO2 emissions for each agent by the MOP method, and Fig. 11 shows transitions by the auction method.
As depicted in Fig. 10, by the MOP method emissions by Building increases linearly, and emissions of Factories 1 and 2 decease as heat demand increases. In this experiment, since CO2 emission basic unit of heat is ﬁxed as a positive value1, emissions by consumers increases as heat demand increases, and producers can reduce their emissions by shifting emissions to the consumer. 1 Actually the value is the same with a basic unit calculated by assuming that Building use its own boiler.
On the other hand, as depicted in Fig. 11, by the auction method emissions by each agent were constant. In the auction method, producers can decide CO2 emission basic unit for their bid. In this experiment, since caps on emissions for each agent was large enough, producers chose zero as CO2 emission basic unit for their bids in order to reduce costs. As a result, CO2 emissions by Factory 1 and 2 stayed at high level, and emissions by Building stayed at low level.
The MOP method at this point does not include a mechanism to change a value of CO2 emission basic unit dynamically. This may cause a situation that results by the MOP becomes worse than the auction method when a cap on emissions for a producer is small. In order to conﬁrm this prospect, the next experiment is done by changing caps on emissions for a producer.
4.5 Ex3: Evaluation on Caps on Emissions Change
Energy demands and caps on CO2 emissions for each agent are shown in Table 9. We ﬁxed the cap on CO2 emissions for Factory 1 as 20000[kg-CO2], and changed the cap for Factory 2.
4.5.1 Comparison on Group Cost
Figure 12 shows transitions of group costs by each method when the cap on emissions for Factory 2 changes.
As depicted in Fig.12, group costs by the MOP method are lower than the costs by the auction method when the caps on emissions for Factory 2 is larger than or equals to 12000[kg-CO2]. The group cost by the auction method, however, becomes low when the capis 11000[kg-CO2].
Figure13 shows transitions of electricity trade of Factory2 by the MOP and the auction methods. When the cap was 11000[kg-CO2], electricity was not traded internally by the MOP method, but was traded by the auction method. Since the MOP method at this point does not include a mechanism to change a value of CO2 emission basic unit dynamically, Factory 2 chose zero as its supply for electricity market when the cap was less than or equals to 12000[kg-CO2]. In the auction method, producers can decide CO2 emission basic unit for their bid. Table 10 show combinations of unit price and CO2 emission basic unit of bids by Factory 2. The table shows that Factory 2 selected a scheme to reduce emissions by setting unit price as zero and emission basic unit as a positive value when the cap was less than or equals to12000[kg-CO2]. As a result, the auction method succeeded to trade electricity internally for every cases.
As described above, we found that the MOP method at this point may lose an opportunity to deal internally in same special cases such as the cap on emissions for a producer is small.
4.6 Ex4: Evaluation on CO2 Emissions Reduction
This experiment is done in order to evaluate possibility of CO2 emissions reduction by the methods. Energy demands and caps on CO2 emissions for each agent are shown in Table 11.
Table 12 shows caps on CO2 emissions for each agent, and CO2 emissions basic units which were used for the MOP method. At ﬁrst, we calculated minimal CO2 emissions by using the individual optimization method for each agent. Values of this emissions were the caps at the ﬁrst step, then the caps are decreased in the same rater %. We evaluated whether each method is able to obtain a feasible solution. In case of the MOP method, we decreased also the CO2 emissions basic unit in the same rate, so that Building meets the cap constraint.
Group costs by each method when emissions basic units in Table 12 were used are shown in Table 13. The whole optimization method succeeded to reduce CO2 emissions of 6% from the individual optimization. This shows that by using internal energy trading it is possible to reduceCO2 of maximally 6% in this case. The auction method succeeded to reduce emissions in 2%, and the MOP method failed to reduce.
In the case of this example, Factories have to operate their gas turbine further to produce electricity for internal trade, and then their emissions increases. On the other hand, since Factories have overly produced heat, internal trade of heat does not increase their emissions. Factories need to shift their emissions onto selling electricity.
Therefore, we set CO2 emissions basic unit of electricity (resp. heat) as 0.502[kg-CO2/kWh] (resp. 0.020[kg-CO2/m3]), and examined again. Results are shown in Table 14. In this case, the MOP method succeeded to reduce emissions in 6%, and the group cost was close to that of the optimal solution. The auction method is not able to reduce further since Factories cannot allow for heat trade. The result shows that the MOP method is effective also for CO2 emissions reduction.
The above discussion suggests to develop CO2 emissions basic unit control mechanism in the MOP method. To do that, we have to develop the following two methods: 1) a method to sense a situation where basic unit should be adjusted, and 2) a method to adjust the basic unit. Our resent research considers how to realize the CO2 emissions basic unit control mechanism (Sugimoto et al., 2008a;b).
6. In Conclusion
This chapter considered energy management in a group which is composed of plural corporate entities. Entities perform optimal planning of purchasing primal energy and operating energy conversion devices in order to satisfy energy demands. Moreover a cap on CO2 emissions is imposed on each entity, and it is not allowed to exhaust CO2 more than their caps. This chapter discussed effectiveness the energy trading in the group. In order to make the problem simple,we supposed the UC problem with only one time period and all of the energy conversion devices were active, and we discussed how to decide energy allocation amongentities. So far, we had proposed anauction based method (Miyamotoetal., 2007), but the method had a problem on efﬁciency. Therefore we proposed the MOP based method for deciding energy allocation. In order to decide energy allocation in DEMSs, we formulated the group, and showed the MOP based execution procedure. Next this chapter compared energy trading decision methods by computational experiments. The proposed MOP method succeeded to obtain better solutions than the previous auction method. We, however, found a necessity to develop CO2 emissions basic unit control mechanism in the MOP method. Directions of next research includes a) the CO2 emissions basic unit control mechanism (Sugimoto et al., 2008a), b) groups with plural consumers (Sugimoto et al., 2008b), and c) planning over plural periods.
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